Estimating Partisan Voting in Nonpartisan Offices Using Cast Vote Records
MIT
May 15, 2024
Partisanship is embedded in who we are (Campbell et al. 1960; Fiorina 1981; Green, Palmquist, and Schickler 2002) and how political parties represent themselves (Aldrich 2011)
Yet, across the U.S., 70% of local governments use nonpartisan election systems where party labels are absent from the ballot (DeSantis and Renner 1991; Svara 2003)
Question
Do patterns in vote choice also fall along a partisan divide in the absence of party labels on the ballot?
Local governments often perform non-ideological work, like paving roads and fixing sewers (Peterson 1981; Oliver, Ha, and Callen 2012; Anzia 2021)
Voter preferences on local issues don’t seem to mirror preferences on national issues (Anzia 2021)
One of the reasons there are conflicting expectations is that measurement of local preferences is extremely difficult (Anzia 2021)
Survey research is limited by sample size, question wording, survey complexity, and inaccurate reporting
Aggregated data must rely on strong ecological inference assumptions
I take a new approach to this problem, using ballot-level data called cast vote records (CVRs)
Standard 2-Parameter Item-Response Theory model (Jackman 2009)
Model
\[ \begin{align*} Y_{j, k(c)} &\sim \text{Categorical}(\pi_{j, k(c)}) \\ \pi_{j, k(c)} &= \text{Pr}(y_{jk} = c | \alpha_j, \gamma_{k(c)}, \beta_{k(c)}) = \text{softmax}(\alpha_j \cdot \gamma_{k(c)} - \beta_{k(c)}) \end{align*} \]
| Quantity | Symbol |
|---|---|
| Individual | \(j = 1, 2, …, J\) |
| Race | \(k = 1, 2, …, K\) |
| Candidate | \(c = 1, 2, …, C\) |
| Ideal point of voter \(j\) | \(\alpha\) |
| Discrimination/Slope Parameter | \(\gamma\) |
| Difficulty/Location Parameter | \(\beta\) |
Identification restrictions are essential Rivers (2003)
Normalize \(\alpha\) to mean 0, standard deviation 1
Let \(\gamma\) vacillate and post-process using the algorithm developed by Papastamoulis and Ntzoufras (2022)
I estimate the model under a Bayesian framework using a bespoke Stan model
Distribution of Ideal Points of Voters for Trump and Biden Voters
Distribution of Ideal Points by State House District in Adams County, Colorado
Different latent dimensions prevent me from directly comparing estimates, instead I can only compare cutpoints
The definition of cutpoints flows from the spatial utility model for a binary choice between \(\zeta_j\) and \(\psi_j\)
\[ \begin{align*} U_i\left(\zeta_j\right) &= -\left\|\xi_i-\zeta_j\right\|^2+\eta_{i j} \\ U_i\left(\psi_j \right) &=- \left\|\xi_i-\psi_j \right\|^2+v_{i j} \end{align*} \]
where \(\xi_i \in \mathbb{R}^d\) is the ideal point of respondent \(i\) and \(\eta_{i j}\) and \(v_{i j}\) are stochastic shocks
The cutpoint is then defined as \(\frac{(\xi_j + \psi_j)}{2}\) , the point at which a respondent would find themselves indifferent between the two candidates
In the categorical model, I compute a series of pairwise comparisons between candidates
Comparison of the Cutpoints from the Categorical 2-Parameter Model and DIME Scores